An Improved Multiquadric Collocation Method for 3-D Electromagnetic Problems

• Published in: IEEE transactions on magnetics Vol. 43; no. 4; pp. 1509 - 1512
• Main Authors: Yong Zhang, Shao, K.R., Youguang Guo, Jianguo Zhu, Xie, D.X., Lavers, J.D.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: New York, NY IEEE 01.04.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 3-D problems; Basis functions; Clouds; Collocation methods; Computational efficiency; Computational geometry; Convergence; Convergence of numerical methods; Cross-disciplinary physics: materials science; rheology; Educational institutions; Exact sciences and technology; Finite element method; Finite element methods; Laplace equations; Magnetism; Materials science; Mathematical analysis; Mathematical models; Meshless method; multiquadric; Nonlinearity; Other topics in materials science; Partial differential equations; Physics; Shape; Solid modeling; 3-D problems; Calculus; multiquadric; Magnetic fields; Meshless method; Magnetic properties
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2007.892479

The multiquadric radial basis function method (MQ RBF or, simply, MQ) developed recently is a truly meshless collocation method with global basis functions. It was introduced for solving many 1- and 2-D partial differential equations (PDEs), including linear and nonlinear problems. However, few works are found for electromagnetic PDEs, especially for 3-D problems. This paper presents an improved MQ collocation method for 3-D electromagnetic problems. Numerical results show a considerable improvement in accuracy over the traditional MQ collocation method, although both methods are direct collocation method with exponential convergence